Compressive full-Stokes polarization and flexible hyperspectral imaging with efficient reconstruction

•Enables four-dimensional imaging in the polarization, spectral and spatial domains.•LCTF plays both a high-resolution hyperspectral filter and a joint linear polarizer.•QWP joins LP to measure full-Stokes parameters of hyperspectral images compressively.•It uses precise solving instead of fuzzy reconstructing the first Stokes parameter.•Improving measurement approach can further separate the last three Stokes parameters.